A Short Course in Computational Geometry and Topology

by Herbert Edelsbrunner

Overview

This monograph presents a short course in computational geometry and topology. In the first part the book covers Voronoi diagrams and Delaunay triangulations, then it presents the theory of alpha complexes which play a crucial role in biology. The central part of the book is the homology theory and their computation, including the theory of persistence which is indispensable for applications, e.g. shape reconstruction. The target audience comprises researchers and practitioners in mathematics, biology, neuroscience and computer science, but the book may also be beneficial to graduate students of these fields.

Product Details

ISBN-13:	9783319059563
Publisher:	Springer International Publishing
Publication date:	04/29/2014
Series:	SpringerBriefs in Applied Sciences and Technology
Edition description:	2014
Pages:	110
Product dimensions:	6.10(w) x 9.25(h) x 0.01(d)

Table of Contents

Roots of Geometry and Topology.- Voronoi and Delaunay Diagrams.- Weighted Diagrams.- Three Dimensions.- Alpha Complexes.- Holes.- Area Formulas.- Topological Spaces.- Homology Groups.- Complex Construction.- Filtrations.- PL Functions.- Matrix Reduction.- Epilogue.